Problem: What's the first wrong statement in the proof below that $ \triangle DEB \cong \triangle CEB$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{EF} \cong \overline{BE}$ $, \ $ $ \angle CEF \cong \angle BED$ $, \ $ $ \angle ECF \cong \angle BDE$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ $ \overline{AC} \cong \overline{DE}$ $, \ $ and $\ $ $ \angle ACB \cong \angle BDE$ Proof $ \triangle DEB \cong \triangle CEF$ because AAS $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle CEF \cong \triangle CAB$ because AAS $ \overline{AC} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle DEB \cong \triangle CAB$ because ASA $ \triangle DEB \cong \triangle CEB$ because SSS
Solution: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle CAB \cong \triangle CEF$ is the first wrong statement.